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(18) A Study on the Analytic Hierarchy Process Using a Fuzzy Reciprocal Matrix
ĦĦĦĦĦĦInternational Association for Statistical Computing 3rd world conference
ĦĦĦĦĦĦon Computational Statistics & Data Analysis,
ĦĦĦĦĦĦp.75, 2005-10
ĦĦThe Analytic Hierarchy Process (AHP) methodology has been widely used in the field of decision making. The classical AHP requires the decision-maker to express his or her preferences through the precise ratio matrix of a preference relation. However, it can often be difficult to express exact estimates of the ratios of importance. Therefore different types of fuzzy extensions to the AHP have been proposed to cope with this problem. One of the most natural uses of fuzzy sets is to employ a reciprocal matrix with fuzzy-valued entries. Fuzzy reciprocal matrices give us flexible specifications of pairwise preference. In this paper, we summarize earlier works and propose an approach to using a fuzzy reciprocal matrix in AHP, as a way of specifying fuzzy restrictions on the possible values of the ratio judgments. Then, it can be computed to what extent there exists a consistent standard AHP matrix which is compatible with these restrictions. An optimal consistency index and optimal weights are derived using a fuzzy constraint satisfaction approach. Further some examples are also shown in our research.
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